Method and apparatus for providing an image to be displayed on a screen

ABSTRACT

The invention relates to a method for providing an image to be displayed on a screen  10  such that a viewer in any current spatial position O in front of the screen  10  can watch the image with only a minimal perspective deformation. According to the invention this is achieved by estimating the current spatial position O of a viewer in relation to a fixed predetermined position Q representing a viewing point in front of the screen  10  from which the image could be watched without any perspective deformation and by providing the image by applying a variable perspective transformation to an originally generated image in response to said estimated current position O of the viewer, such that the viewer in said position O is enabled to watch the image without a perspective deformation.

[0001] The invention relates to a method and an apparatus for providingan image to be displayed on a screen, in particular on a TV screen or ona computer monitor, according to the preambles of claims 1, 12 and 16.

[0002] Such a method and apparatus are known in the art. However, inprior art it is also known that perspective deformations may occur whenan image is displayed on a screen depending on the current position of aviewer watching the screen. That phenomenon shall now be explained indetail by referring to FIG. 3.

[0003]FIG. 3 is based on the assumption that a 2-dimensional image of a3-dimensional scene is either taken by a camera, e.g. a TV camera orgenerated by a computer graphic program, e.g. a computer game. Moreover,an assumption is made about the location of the centre of the projectionP and the rectangular viewport S of the original image, wherein P and Srelate to the location where the original image is generated, e.g. acamera, but not necessarily to the location where it is later watched bya viewer. P and S are considered to form a fictive first pyramid asshown in FIG. 3. In the case that the image is taken with a camera, P isthe optical centre of this camera and S is its light sensitive area. Inthe case that the image is generated by a computer graphic theparameters P and S can be considered as parameters of a virtual camera.

[0004] The original image might be generated by the camera or by thecomputer program by using different transformations known in the art:

[0005] One example for such a transformation is the change of theviewing point from which a particular scene is watched by the real orvirtual camera.

[0006] Another example for such a transformation is the following oneused in computer graphic applications for correcting texture mapping.Such a transformation may be described according to the followingequation: $\begin{matrix}{\begin{bmatrix}x \\y\end{bmatrix} = {\begin{bmatrix}{{a\quad u} + {bv} + c} \\{{du} + {ev} + f}\end{bmatrix}/\left( {{gu} + {hv} + i} \right)}} & (1)\end{matrix}$

[0007] wherein:

[0008] the term (gu+hv+i) represents a division per pixel;

[0009] u,v are the co-ordinates of a pixel of the image beforetransformation;

[0010] x,y are the co-ordinates of the pixel of the image after thetransformation; and

[0011] a,b,c,d,e,f,g,h and i are variable coefficients beingindividually defined by the graphic program.

[0012] However, irrespective as to whether the original image has beengenerated by conducting such transformations or not or as to whether theimage has been generated by a camera or by a computer program, there isonly one spatial position Q in the location where the image is laterwatched after its generation, i.e. in front of a screen 10 on which theimage is displayed, from which a viewer can watch the image on thescreen without any perspective deformations.

[0013] Said position Q is fix in relation to the position of the screen10 and can be calculated form the above-mentioned parameters P and Saccording to a method known in the art.

[0014] The position Q is illustrated in FIG. 3 as the top of a secondfictive pyramid which is restricted by an rectangular area A of theimage when being displayed on the screen 10. Said position Q, that meansthe ideal position for the viewer, is reached when the second fictivepyramid is similar to the first pyramid.

[0015] More specifically, the first and the second pyramid are similarif the following two conditions are fulfilled simultaneously:

[0016] a) Q lies on a line L which is orthogonal to the area A of thedisplayed image and goes through the centre of A; and

[0017] b) the distance between Q and the centre of A is such that thetop angles of the two pyramids are equal.

[0018] If condition a) is not fulfilled there will be an oblique secondpyramid; if condition b) is not fulfilled there will be an erroneousperspective shortening in case of occulsion, i.e. different objects ofthe original 3D scene get false relative apparent depths. The case thatthe condition a) is not fulfilled is more annoying to the viewer thanthe case that condition b) is not fulfilled.

[0019] Expressed in other words, if the current position O of the viewerwatching the image on the screen 10 does not correspond to the positionQ, i.e. if there is a distance |Q-O| between said positions Q and O, theviewer will see a perspectively deformed image. A large distance |Q-O |can result in reduced visibility of the displayed image and worse inreduced readability of text.

[0020] In prior art a suboptimal approach is known to overcome thesedisadvantages by adapting the displayed image to the current position ofthe viewer. More specifically, that approach proposes to rotate thephysical screen by hand or by an electric motor such that condition a)is fulfilled; e.g. Bang & Olufsen sells a TV having a motor for rotatingthe screen.

[0021] According to that approach rotation of the screen is controlledin response to the distance |0-Q | between the position O of the viewerand the fix position Q. Rotation of the screen by hand is inconvenientfor the viewer and the rotation by motor is expensive and vulnerable.Moreover, condition b) can not be fulfilled by that approach.

[0022] Starting from that prior art it is the object of the invention toimprove a method and apparatus for providing an image to be displayed ona screen such that the application of the method is more convenient to auser or a viewer of the image.

[0023] Said object is solved by the method according to claim 1comprising the steps of estimating the current spatial position O of aviewer in relation to a fixed predetermined position Q representing aviewing point in front of the screen from which the image could bewatched without any perspective deformation; and providing the image byapplying a variable perspective transformation to an originallygenerated image in response to said estimated current position O of theviewer.

[0024] Advantageously said perspective transformation enables a viewerin any current spatial position O in front of the screen to watch theimage on the screen without perspective deformations. Consequently, thevisibility of the displayed image and in particular the readability ofdisplayed text is improved.

[0025] Said transformation is convenient to the viewer because he doesnot get aware of an application of the transformation when he iswatching the images on the screen. There is no physical movement of thescreen like in the prior art.

[0026] Moreover, the implementation of the transformation can berealised cheaply and usually no maintenance is required.

[0027] The application of said method is in particular helpful for largescreen TV's or large monitors.

[0028] According to an embodiment of the invention the perspectivetransformation of the original image advantageously includes a rotationand/ or a translation of the co-ordinates of at least one pixel of theoriginally generated image. In that case an exact transformation of theposition of the viewer into the ideal position Q can be achieved andperspective deformations can completely be deleted.

[0029] Preferably, the estimation of the position O of the viewer isdone by tracking the head or the eye of the viewer.

[0030] Alternatively, said estimation is done by estimating the currentposition of a remote control used by the viewer for controlling thescreen.

[0031] Preferably, the method steps of the method according to theinvention are carried out in real-time because in that case the vieweris not optically disturbed when watching the image on the screen.

[0032] Further advantageous embodiments of the method according to theinvention are subject matter of the dependent claims.

[0033] The object of the invention is further solved by an apparatusaccording to claim 12. The advantages of said apparatus correspond tothe advantages outlined above with regard to the method of theinvention.

[0034] Advantageously, the estimation unit and/ or the correcting unitis included in a TV set or alternatively in a computer. In these cases,there are no additional unit required which would otherwise have to beplaced close to the TV set or to the computer.

[0035] The object of the invention is further solved by the subjectmatter of claim 16, the advantages of which correspond the advantages ofthe apparatus described above.

[0036] In the following a preferred embodiments of the invention will bedescribed by referring to the accompanying figures, wherein:

[0037]FIG. 1 shows an apparatuses for carrying out a method according tothe invention;

[0038]FIG. 2 illustrates the watching of an image on a screen withoutperspective deformations according to the invention; and

[0039]FIG. 3 illustrates the watching of an image on a screen from anideal position Q without any perspective deformations as known in theart.

[0040]FIG. 1 shows an apparatus 1 according to the present invention. Itincludes an estimation unit 20 for estimating the current spatialposition O of a viewer in front of the screen 10 in relation to a fixedpredetermined position Q representing a viewing point in front of thescreen from which a provided image could be watched without anyperspective deformation and for outputting a respective positioningsignal.

[0041] The apparatus 1 further includes a correction unit 30 forproviding the image by correcting the perspective deformation of anoriginally generated image in response to said estimated currentposition O and for outputting an image signal representing the providedimage having no perspective deformation to the screen 10.

[0042] The correction unit 30 carries out the correction of theperspective deformation by applying a variable perspectivetransformation to the original image generated e.g. in a camera or by acomputer graphic program.

[0043] The transformation is represented by formula (1) known in the artas described above. The usage of said transformation does not change afix position Q from which the image can be watched after its generationwithout any perspective deformations.

[0044] It is important to note that the location where the originalimage is generated and the location where said image is later watched ona TV-screen or on a monitor are usually different. Moreover, at the timewhen the original image is generated a current or actual position O of aviewer in front of the screen when watching the image is not known andcan thus not be considered when generating the original image.

[0045] Based on that situation the invention teaches another applicationof the known transformation according to equation 1. More specifically,according to the invention said transformation is used to enable aviewer to watch the image not only from the position Q but from anyarbitrary position O in front of the screen 10 with only a minimalperspective deformation. In the case that the original image has beengenerated by conducting the transformation, the invention teaches anadditional or second application of said transformation in order togenerate the displayed image.

[0046] More specifically, according to the invention the variablecoefficients a,b,c,d,e,f,g,h and i of said transformation are adapted inresponse to the currently estimated position O of the viewer. Thetransformation with the such adapted coefficients is subsequentlyapplied to the original image in order to provide the image to bedisplayed on the screen. Said displayed image can be watched by theviewer from any position in front of the screen 10 without perspectivedeformations.

[0047] A method for carrying out the adaptation will now be explained indetail by referring to FIG. 2. In FIG. 2 a situation is shown in which aviewer watches the screen 10 from a position O which does not correspondto the ideal position Q. The meanings of the parameters A, L, S, O, P, Qin FIG. 2 correspond to their respective meanings as explained above byreferring to FIG. 3. The method comprises the steps of:

[0048] 1. Defining a co-ordinate system with Q as origin in which thex-axis lies in a horizontal direction, in which the y-axis lies in thevertical direction and in which the z-axis also lies in the horizontaldirection leading from the position Q through the centre of the area Aof the image displayed on the screen 10.

[0049] 2. The parameters u and v as used in the transformation accordingto equation (1) relate to an only two-dimensional Euclidian co-ordinatesystem having its origin in the centre of the area A. For later beingable to calculate the coefficients a-i of the transformation, theco-ordinates u and v are transformed from said two-dimensional Euclidianspace into a three-dimensional Euclidian space having Q as originaccording to the following equation: $\begin{matrix}{\left. \begin{pmatrix}u \\v\end{pmatrix}\leftrightarrow\begin{pmatrix}u \\v \\L_{d}\end{pmatrix} \right.,} & (2)\end{matrix}$

[0050] wherein L_(d) is the distance between the position Q and thecentre of the image area A.

[0051] 3. The co-ordinates (u, v, L_(d)) of the displayed image in thethree-dimensional Euclidian space are further transformed into athree-dimensional projective space having Q as origin according to$\begin{matrix}\left. \begin{pmatrix}u \\v\end{pmatrix}\leftrightarrow\begin{pmatrix}u \\v \\L_{d}\end{pmatrix}\leftrightarrow{\begin{pmatrix}u \\v \\L_{d} \\1\end{pmatrix}.} \right. & (3)\end{matrix}$

[0052] 4.Subsequently, an Euclidian transformation T is calculated tochange the co-ordinate system such that the viewer position O is madethe centre of the new co-ordinate system. Said Euclidian transformationT is in general calculated according to: $\begin{matrix}{{\begin{bmatrix}0 \\0 \\0 \\1\end{bmatrix} = {{\begin{bmatrix}R_{11} & R_{12} & R_{13} & t_{x} \\R_{21} & R_{22} & R_{23} & t_{y} \\R_{31`} & R_{32} & R_{33} & t_{z} \\0 & 0 & 0 & 1\end{bmatrix}\quad\begin{bmatrix}x_{0} \\y_{0} \\z_{0} \\1\end{bmatrix}} = {T\begin{bmatrix}x_{0} \\y_{0} \\z_{0} \\1\end{bmatrix}}}},} & (4)\end{matrix}$

[0053] wherein:

[0054] the vector [x₀, y₀ z₀, 1] represents the co-ordinates of theposition O of the viewer in the three-dimensional projective spacehaving Q as origin,

[0055] R_(ij) with i=1−3 and j=1−3 represent the co-ordinates of arotation matrix for rotating the co-ordinates, e.g. through φ,

[0056] t_(x), t_(y) and t_(Z) form a translation vector representing atranslation of the co-ordinates, and

[0057] the vector [0, 0, 0, 1] represents the origin of the newco-ordinate system corresponding to the position O of the viewer.

[0058] 5. The found transformation T is now applied to all the pixels ofthe rectangle area A, i.e. to the pixel co-ordinates of the displayedimage, according to $\begin{matrix}{\begin{bmatrix}x_{TR} \\y_{TR} \\z_{TR} \\1\end{bmatrix} = {{\begin{bmatrix}R_{11} & R_{12} & R_{13} & t_{x} \\R_{21} & R_{22} & R_{23} & t_{y} \\R_{31`} & R_{32} & R_{33} & t_{z} \\0 & 0 & 0 & 1\end{bmatrix}\quad\begin{bmatrix}u \\v \\L_{d} \\1\end{bmatrix}} = {{T\begin{bmatrix}u \\v \\L_{d} \\1\end{bmatrix}}.}}} & (5)\end{matrix}$

[0059] Equation 5 represents a transformation of the pixel co-ordinates[u, v, L_(d), 1] of the image on the screen in a co-ordinate systemhaving Q as origin into the transformed pixel co-ordinates [x_(TR),y_(TR), z_(TR), 1] of said image into the co-ordinate system having theposition O of the viewer as the origin. Both vectors [u, v, L_(d), 1]and [x_(TR), y_(TR), zTR, 1] lie in the three-dimensional projectivespace.

[0060] 6. In the next method step, the transformed pixel positionsresulting from equation 5 are transformed by applying a perspectiveimage transformation to them. Said perspective image transformationserves for transforming the transformed co-ordinates [x_(TR), y_(TR),z_(TR), 1] in the three-dimensional projective space into co-ordinates[unew, Vnew, wnew] in a two-dimensional projective space according to:$\begin{matrix}{\begin{bmatrix}u_{new} \\v_{new} \\w_{new}\end{bmatrix} = {\begin{bmatrix}L_{d} & 0 & 0 & 0 \\0 & L_{d} & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad\begin{bmatrix}x_{TR} \\y_{TR} \\z_{TR} \\1\end{bmatrix}}} & \left( 6^{\prime} \right) \\{{= {{\begin{bmatrix}L_{d} & 0 & 0 & 0 \\0 & L_{d} & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad\begin{bmatrix}R_{11} & R_{12} & R_{13} & t_{x} \\R_{21} & R_{22} & R_{23} & t_{y} \\R_{31`} & R_{32} & R_{33} & t_{z} \\0 & 0 & 0 & 1\end{bmatrix}}\quad\begin{bmatrix}u \\v \\L_{d} \\1\end{bmatrix}}};} & \left( 6^{''} \right) \\{= {\begin{bmatrix}L_{d} & 0 & 0 & 0 \\0 & L_{d} & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix} \cdot \begin{bmatrix}{{R_{11}u} + {R_{12}v} + {R_{13}L_{d}} + t_{x}} \\{{R_{21}u} + {R_{22}v} + {R_{23}L_{d}} + t_{y}} \\{{R_{31}u} + {R_{32}v} + {R_{33}L_{d}} + t_{z}} \\1\end{bmatrix}}} & \left( 6^{\prime\prime\prime} \right) \\{= \begin{bmatrix}{{R_{11}L_{d}u} + {R_{12}L_{d}v} + {R_{13}L_{d}^{2}} + {L_{d}t_{x}}} \\{{R_{21}L_{d}u} + {R_{22}L_{d}v} + {R_{23}L_{d}^{2}} + {L_{d}t_{y}}} \\{{R_{31}u} + {R_{32}v} + {R_{33}L_{d}} + t_{z}}\end{bmatrix}} & \left( 6^{I\quad V} \right) \\{\begin{bmatrix}{L_{d}R_{11}} & {L_{d}R_{12}} & {{L_{d}^{2}R_{13}} + {L_{d}t_{x}}} \\{L_{d}R_{21}} & {L_{d}R_{22}} & {{L_{d}^{2}R_{23}} + {L_{d}t_{y}}} \\R_{31} & R_{32} & {{L_{d}R_{33}} + t_{z}}\end{bmatrix}\quad\begin{bmatrix}u \\v \\1\end{bmatrix}} & \left( 6^{V} \right) \\{\left. \Leftrightarrow\begin{bmatrix}u_{new} \\v_{new} \\w_{new}\end{bmatrix} \right. = {\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix}\quad\begin{bmatrix}u \\v \\1\end{bmatrix}}} & \left( 6^{V\quad I} \right)\end{matrix}$

[0061] 7. The vector [u_(new), v_(new), w_(new)] in the two-dimensionalprojective space can be transformed into the vector [x, y] in thetwo-dimensional Euclidian space according to $\begin{matrix}{\left. \begin{bmatrix}u_{new} \\v_{new} \\w_{new}\end{bmatrix}\rightarrow\begin{bmatrix}{u_{new}/w_{new}} \\{y_{new}/w_{new}}\end{bmatrix} \right. = \begin{bmatrix}x \\y\end{bmatrix}} & (7)\end{matrix}$

[0062] 8. Thus, equation 6^(VI) can—under consideration of equation 7-betransformed into the 2-dimensional Euclidian space according to:$\begin{matrix}{\begin{bmatrix}x \\y\end{bmatrix} = {{\begin{bmatrix}a & b & c \\d & e & f\end{bmatrix}\quad\begin{bmatrix}u \\v \\1\end{bmatrix}}/{\begin{bmatrix}g & h & i\end{bmatrix}\quad\begin{bmatrix}u \\v \\1\end{bmatrix}}}} & \left( 8^{\prime} \right) \\{= {\begin{bmatrix}{{a\quad u} + {bv} + c} \\{{du} + {ev} + f}\end{bmatrix}/\left\lbrack {{gu} + {hv} + i} \right\rbrack}} & \left( 8^{''} \right)\end{matrix}$

[0063] It is important to note that equation 8″ corresponds to equation1!!

[0064] 9. Consequently, the variable coefficients a-i of thetransformation according to equation 1 can be calculated by comparingequation 6^(VI), with equation 6^(V) according to: $\begin{matrix}{{\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix}\quad\begin{bmatrix}{L_{d}R_{11}} & {L_{d}R_{12}} & {{L_{d}^{2}R_{13}} + {L_{d}t_{x}}} \\{L_{d}R_{21}} & {L_{d}R_{22}} & {{L_{d}^{2}R_{23}} + {L_{d}t_{y}}} \\R_{31} & R_{32} & {{L_{d}R_{33}} + t_{z}}\end{bmatrix}}.} & (9)\end{matrix}$

[0065] Method steps 1 to 9 and in particular equation 9 are in generalknown in the art from texture mapping in computer graphics application.

[0066] However, in difference to the prior art, according to the presentinvention the coefficients a-i according to equation 9 are calculatedinter alia from the estimated current position of the viewer O in frontof the screen 10 of a TV set or of a monitor.

[0067] Equation 9 represents an exact transformation including ingeneral a rotation and a translation such that it compensates for anyarbitrary position O of the viewer.

[0068] More specifically, L_(d) is fix and the parameters R_(ij), t_(x),t_(y) and t_(Z) can be calculated from the original image area A on thescreen 10, from the position Q and from the estimated position O of theviewer. Further, having calculated the right side of equation 9, alsothe coefficients a-i of the perspective transformation on the left sideof equation 9 are known.

[0069] In the following, two simple examples for applying theperspective transformation, i.e. for calculating the coefficients a-i,according to the present invention are provided.

[0070] In a first example it is assumed that a viewer O stays on theline L connecting the centre of the area A of the screen with theposition Q in front of the screen. In that case a rotation of the imageto be displayed is obsolete; only a translative transformation isrequired.

[0071] With equation 1 and the calculated coefficients a-i it ispossible to compensate for an eye-position O of the viewer on the line Lcloser to the area A than to the position Q, but in that case some ofthe outer area of the received image is not displayed. Or it is possibleto compensate for an eye-position O of the viewer on the line L furtheraway from the area A than to the position Q, but in that case some ofthe outer area of the screen is not used.

[0072] In the second example, it is assumed that the viewer O does notstay on the line L but having a distance to the centre of the area Awhich corresponds to the distance between Q and said centre.Consequently, the translation tx, ty and tz coefficients in equation 9can be ignored and only correction for the horizontal rotation needs tobe considered. The required perspective transformation follows from thepyramid with O as top and with a line through the position O of theviewer and the centre of the screen as centre line.

[0073] According to FIG. 2 rotation around the position Q is required toget the position O of the viewer onto the line L, after the position Ois projected on a horizontal plane through Q (thus, ignoring they-co-ordinate of the position O ). This gives: $\begin{matrix}{{\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix} = \begin{bmatrix}{L_{d}\cos \quad \phi} & 0 & {{- L_{d}^{2}}\sin \quad \phi} \\0 & L_{d} & 0 \\{\sin \quad \phi} & 0 & {L_{d}\cos \quad \phi}\end{bmatrix}}{with}{{\cos \quad \phi} = {z_{0}/\left( \sqrt{x_{0}^{2} + z_{0}^{2}} \right)}}{and}} & (10) \\{{\sin \quad \phi} = {x_{0}/\left( \sqrt{x_{0}^{2} + z_{0}^{2}} \right)}} & (11)\end{matrix}$

[0074] wherein x₀ and z₀ represent the co-ordinates of the viewer in theEuclidian space in a co-ordinate system having Q as origin.

[0075] The rotation around Q changes the distance to the centre of A,but after the rotation a scaling is required to avoid that either a partof the transformed image is outside the display screen or that a largepart of the display screen is not used: $\begin{matrix}{\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix} = {\begin{bmatrix}s & 0 & 0 \\0 & s & 0 \\0 & 0 & 1\end{bmatrix}\begin{bmatrix}{L_{d}\cos \quad \phi} & 0 & {{- L_{d}^{2}}\sin \quad \phi} \\0 & L_{d} & 0 \\{\sin \quad \phi} & 0 & {L_{d}\cos \quad \phi}\end{bmatrix}}} & (12)\end{matrix}$

[0076] The scale factor can be computed by requiring that theperspective projections of the four corners of the original rectangle Aare on the four boundaries of the rectangle: $\begin{matrix}{\begin{bmatrix}x_{left} \\y\end{bmatrix} = {P\left( {s,u_{left},v_{bottom}} \right)}} & (13) \\{\begin{bmatrix}x \\y_{bottom}\end{bmatrix} = {P\left( {s,u_{left},v_{bottom}} \right)}} & (14) \\{\begin{bmatrix}x_{left} \\y\end{bmatrix} = {P\left( {s,u_{ueft},v_{top}} \right)}} & (15) \\{\begin{bmatrix}x \\y_{top}\end{bmatrix} = {P\left( {s,u_{left},v_{top}} \right)}} & (16) \\{\begin{bmatrix}x_{right} \\y\end{bmatrix} = {P\left( {s,u_{right},v_{bottom}} \right)}} & (17) \\{\begin{bmatrix}x \\y_{bottom}\end{bmatrix} = {P\left( {s,u_{right},v_{bottom}} \right)}} & (18) \\{\begin{bmatrix}x_{right} \\y\end{bmatrix} = {P\left( {s,u_{right},v_{top}} \right)}} & (19) \\{\begin{bmatrix}x \\y_{top}\end{bmatrix} = {P\left( {s,u_{right},v_{top}} \right)}} & (20)\end{matrix}$

[0077] with P(s,u,v) being a rational perspective transformation derivedfrom the right side of equation 12 in the same way as equation 8′ isderived from equation 6^(VI). The variables u and v are 2-dim. Euclideanco-ordinates of positions on the screen.

[0078] This gives eight scale factors si i=1−8. The smallest one shouldbe used as the final or optimal scale factor in equation 12 ensuringthat the area of the transformed image completely fits into the area ofthe screen on which it shall be displayed.

[0079] The co-ordinates x and y on both sides of equations 13 to 20represent co-ordinates of the image area A in the two-dimensionalEuclidian space. Equations 13 to 20 express conditions or requirementsfor the position of the corners of a new area Anew of the image aftertransformation. E.g. in equation 13 it is required that thex-co-ordinate of the corner of the original rectangle A represented bythe co-ordinates x_(left) and y_(bottom) is kept identical aftertransformation.

[0080] Returning back to equation 1 and FIG. 2 it shall be pointed outthat an application of the perspective transformation according toequation 1 onto an originally generated image ensures that the pyramidformed by the position Q and the original area A of the image on thescreen 10 is similar to the pyramid formed by the transformed areaA_(new) of the image and the estimated position O of the viewer. This isillustrated in FIG. 2.

[0081] The proposed solution may be implemented in future TV's which areextended with means for special grapic effects inclusive cheap hardwarefor carrying out the required calculations according to the inventionwith only little additional costs.

1. Method for providing an image to be displayed on a screen (10), inparticular on a TV screen or on a computer monitor, the method beingcharacterized by the following steps of: estimating the current spatialposition O of a viewer in relation to a fixed predetermined position Qrepresenting a viewing point in front of the screen (10) from which theimage could be watched without any perspective deformation; andproviding the image by applying a variable perspective transformation toan originally generated image in response to said estimated currentposition O of the viewer, such that the viewer in said position O isenabled to watch the image without a perspective deformation.
 2. Themethod according to claim 1, characterized in that the transformation iscarried out according to the following formula: $\begin{bmatrix}x \\y\end{bmatrix} = {\begin{bmatrix}{{a\quad u} + {bv} + c} \\{{du} + {ev} + f}\end{bmatrix}/\left( {{gu} + {hv} + i} \right)}$

wherein: u,v are the co-ordinates of a pixel of the original imagebefore transformation; x,y are the co-ordinates of the pixel of theprovided image after the transformation; and a,b,c,d,e,f,g,h and i arevariable coefficients defining the transformation and being adapted inresponse to the estimated current position O of the viewer.
 3. Themethod according to claim 1 or 2, characterized in that the imagecomprises at least one pixel.
 4. The method according to one of thepreceding claims, characterized in that the transformation comprises arotation and/ or a translation of the co-ordinates of the at least onepixel of the image.
 5. The method according to claim 4, characterized inthat the variable coefficients a,b,c,d,e,f,g,h and i are calculatedaccording to: $\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix} = \begin{bmatrix}{L_{d}R_{11}} & {L_{d}R_{12}} & {{L_{d}^{2}R_{13}} + {L_{d}t_{x}}} \\{L_{d}R_{21}} & {L_{d}R_{22}} & {{L_{d}^{2}R_{23}} + {L_{d}t_{y}}} \\R_{31} & R_{32} & {{L_{d}R_{33}} + t_{z}}\end{bmatrix}$

wherein: L_(d) is the fixed distance between the position Q and thecentre of an area A of the image when being displayed on the screen;R_(ij) with i=1−3 and j=1−3 are the coefficients of a rotation matrixfor rotating the pixels; t_(x), t_(y) and t_(z) are the coefficients ofa translation vector; and wherein the rotation matrix and thetranslation vector are calculated according to the estimated currentspatial position O of the viewer in relation to the position Q.
 6. Themethod according to claim 5, characterized in that in the case that thetranslation is ignored and that rotation is considered to take placeonly in a plane defined by the positions O, Q and a line L connecting Qand being orthogonal to the area A of the displayed image on the screen,the variable coefficients a,b,c,d,e,f;g,h and i are calculated accordingto: $\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix} = \begin{bmatrix}{L_{d}\cos \quad \phi} & 0 & {{- L_{d}^{2}}\sin \quad \phi} \\0 & L_{d} & 0 \\{\sin \quad \phi} & 0 & {L_{d}\cos \quad \phi}\end{bmatrix}$

wherein: R_(1l)=R₃₃=cosφ, R₁₃=−sinφ, R₃₁=sinφ; and t_(x)=t_(y)=t_(z)=0with:${{\cos \quad \phi} = {{{z_{0}/\sqrt{x_{0}^{2} + z_{0}^{2}}}\quad {and}\quad \sin \quad \phi} = {x_{0}/\sqrt{x_{0}^{2} + z_{0}^{2}}}}}\quad$

wherein x₀ and z₀ are co-ordinates of the viewer position in aco-ordinate sytem having Q as origin.
 7. The method according to claim6, characterized in that the step of calculating the variablecoefficients a,b,c,d,e,f,g,h and i further comprises a scaling of thecoefficients with a scale factor s according to: $\begin{bmatrix}a & b & c \\d & e & f \\g & h & i\end{bmatrix} = {{\begin{bmatrix}s & 0 & 0 \\0 & s & 0 \\0 & 0 & 1\end{bmatrix}\begin{bmatrix}{L_{d}\cos \quad \phi} & 0 & {{- L_{d}^{2}}\sin \quad \phi} \\0 & L_{d} & 0 \\{\sin \quad \phi} & 0 & {L_{d}\cos \quad \phi}\end{bmatrix}} = {{P(s)}.}}$


8. The method according to claim 7, characterized in that an optimalscale factor which is chosen such that the provided image completelyfits into the area of the screen is determined by carrying out thefollowing steps: calculating preliminary scale factors si i=1−8 bysolving the following 8 linear equation systems:${{{{{{{{{{{{\begin{bmatrix}x_{left} \\y\end{bmatrix} = {P\left( {s,u_{left},v_{bottom}} \right)}};}\quad\begin{bmatrix}x \\y_{bottom}\end{bmatrix}} = {{{P\left( {s,u_{left},v_{bottom}} \right)}\begin{bmatrix}x_{left} \\y\end{bmatrix}} = {P\left( {s,u_{left},v_{top}} \right)}}};}\quad\begin{bmatrix}x \\y_{top}\end{bmatrix}} = {{{P\left( {s,u_{left},v_{top}} \right)}\begin{bmatrix}x_{right} \\y\end{bmatrix}} = {P\left( {s,u_{right},v_{bottom}} \right)}}};}\quad\begin{bmatrix}x \\y_{bottom}\end{bmatrix}} = {{{P\left( {s,u_{right},v_{bottom}} \right)}\begin{bmatrix}x_{right} \\y\end{bmatrix}} = {P\left( {s,u_{right},v_{top}} \right)}}};}\quad\begin{bmatrix}x \\y_{top}\end{bmatrix}} = {P\left( {s,u_{right},v_{top}} \right)}$

wherein the x,y vectors on the right side of each of said linear systemsrepresent the fictive co-ordinates of a corner of the original image onthe screen, wherein the x,y vectors on the left side respectivelyrepresents the co-ordinate of a corner of the provided image actuallydisplayed on the screen, and wherein the co-ordinates x_(right),x_(left), y_(bottom) and y_(top) are predetermined; and selecting theminimal one of said calculated preliminary scale factors si as theoptimal scale factor.
 9. The method according to one of the precedingclaims, characterized in that the estimation is done by tracking thehead or the eye of the viewer.
 10. The method according to one of claims1 to 9, characterized in that the estimation of the position O is doneby estimating the current position of a remote control used by theviewer for controlling the screen.
 11. The method according to one ofthe preceding claims, characterized in that the steps of the method arecarried out in real-time.
 12. Apparatus (1) for providing an image to bedisplayed on a screen (10), in particular on a TV screen or on acomputer monitor, the apparatus is characterized by: an estimation unit(20) for outputting a positioning signal representing an estimation of acurrent spatial position O of a viewer in front of the screen (10) inrelation to a fixed predetermined position Q representing a viewingpoint from which the image on the screen (10) can be watched without anyperspective deformation; and a correcting unit (30′) for applying avariable perspective transformation to an originally generated image inresponse to said positioning signal such that the viewer in the positionO is enabled to watch the image without said perspective deformation.13. The apparatus according to claim 12, characterized in that thetransformation is represented by the following formula: $\begin{matrix}{\begin{bmatrix}x \\y\end{bmatrix} = {\begin{bmatrix}{{a\quad u} + {bv} + c} \\{{du} + {ev} + f}\end{bmatrix}/\left( {{gu} + {hv} + i} \right)}} & (1)\end{matrix}$

wherein: u,v are the co-ordinates of a pixel of the original imagebefore transformation; x,y are the co-ordinates of the pixel of theprovided image after the transformation; and a,b,c,d,e,f,g,h and i arevariable coefficients defining the transformation and being adapted inresponse to the estimated current position O of the viewer such that theviewer in any current spatial position O is enabled to watch the imageon the screen (10) without perspective deformations.
 14. The apparatus(1) according to claim 13, characterized in that the estimation unitand/or the correcting unit is included in a TV set.
 15. The apparatus(1) according to claim 14, characterized in that the estimation unitand/ or the correcting unit is included in a computer.
 16. A correctingunit (30) being characterized in that it is adapted to apply a variableperspective transformation to an originally generated image in order toprovide an image to be displayed on a screen (10) such that a viewer inany current spatial position O in front of the screen (10) is enabled towatch the provided image on the screen (10) without a perspectivedeformation.
 17. The correcting unit (30) according to claim 16,characterized in that the transformation is represented by the followingformula: $\begin{bmatrix}x \\y\end{bmatrix} = {\begin{bmatrix}{{a\quad u} + {bv} + c} \\{{du} + {ev} + f}\end{bmatrix}/\left( {{gu} + {hv} + i} \right)}$

wherein: u,v are the co-ordinates of a pixel of the original imagebefore transformation; x,y are the co-ordinates of the pixel of theprovided image after the transformation; and a,b,c,d,e,f,g,h and i arevariable coefficients defining the transformation and being adapted inresponse to the estimated current position O of the viewer.